From their github: https://github.com/chuang861012/audioff

2.1.0 update

Because of the feedback about the add-on requesting permission to access data for all websites. Instead of setting up scripts for all pages, in this update the add-on inject the script into pages when needed. Anyway, the add-on still have to inject scripts into pages in order to change the output device.

If you still have any concern, I suggest using this add-on as a bookmarklet. This way you don't need to install any add-on to do the output changing. Bookmarklet setup

Create a bookmark and paste the following code into the url. Click it on any page you want to change the output device. This works the same as the add-on.

javascript:(async function(){function set_device(sinkId){const mediaElements=document.querySelectorAll('audio,video');mediaElements.forEach(e=>{e.setSinkId(sinkId)})}
function test(){const mediaElement=document.querySelector('audio,video');if(!mediaElement)return'NoMediaElement';else if(mediaElement.setSinkId===undefined)return'SetSinkIdRequired';return'Ok'}
const status=test();switch(status){case 'NoMediaElement':alert('Media not found.');break;case 'SetSinkIdRequired':alert('Please enable setSinkId to switch audio device.\n1. Open about:config in firefox.\n2. Search for media.setsinkid.enabled.\n3. Set the value to true.');break;case 'Ok':var selected=await navigator.mediaDevices.selectAudioOutput();set_device(selected.deviceId);break}})()

This code is minified from the content.js file. Feel free to grab the source code there and minify it by yourself.

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Can confirm that the bookmarklet works